On the other hand, FA needs much more time to search for the best solution and its performance significantly deteriorates with the increases selleck chemicals in population size. In HS/FA, top fireflies scheme is introduced to reduce running time. This scheme is carried out by reduction of outer loop in FA. Through top fireflies scheme, the time complexity of HS/FA decreases from O(NP2) to O(KEEPNP), where KEEP is the number of top fireflies. The proposed approach is evaluated on various benchmarks. The results demonstrate that the HS/FA performs more effectively and accurately than FA and other intelligent algorithms.The rest of this paper is structured below. To begin with, a brief background on the HS and FA is provided in Sections 2 and 3, respectively. Our proposed HS/FA is presented in Section 4.

HS/FA is verified through various functions in Section 5, and Section 6 presents the general conclusions.2. HS MethodAs a relative optimization technique, there are four optimization operators in HS [17, 48, 49]: HM: the harmony memory, as shown in (1); HMS: the harmony memory size, HMCR: the harmony memory consideration rate, PAR: the pitch adjustment rate, and bw: the pitch adjustment bandwidth [1].ConsiderHM=[x11x21?xD1x12x22?xD2????x1HMSx2HMS?xDHMS|fitness?(x1)fitness?(x2)?fitness?(xHMS)].(1)The HS method can be explained according to the discussion of the player improvisation process. There are 3 feasible options for a player in the music improvisation process: (1) play several pitches that are the same with the HMCR; (2) play some pitches like a known piece; or (3) improvise new pitches [1].

These three options can be idealized into three components: use of HM, pitch adjusting, and randomization [1]. Similar to selecting the optimal ones in GA, the first part is important as it is [1]. This can guarantees that the optimal harmonies will not be destroyed in the HM. To make HS more powerful, the parameter HMCR should be properly set [1]. Through several experiments, in most cases, HMCR = 0.7~0.95.The pitch in the second part needs to be adjusted slightly; and hence a proper method is used to adjust the frequency [1]. If the new pitch xnew is updated byxnew=xold+bw(2��?1),(2)where �� is a random number in [0,1] and xold is the current pitch. Here, bw is the bandwidth.Parameter PAR should also be appropriately set.

If PAR is very close to 1, then the solution is always updating and HS is GSK-3 hard to converge. If it is next to 0, then little change is made and HS may be premature. So, here we set PAR = 0.1~0.5 [1]. To improve the diversity, the randomization is necessary as shown in the third component. The usage of randomization allows the method to go a step further into promising area so as to find the optimal solution [1].The HS can be presented in Algorithm 1. Where D is the number of decision variables.